Solve the system of equations: $x - y = -1$ $x^2 + y = 1$

1. Problem Description

Solve the system of equations:

$x - y = -1$

$x^2 + y = 1$

2. Solution Steps

From the first equation, we can express $y$ in terms of $x$:

$x - y = -1$

$y = x + 1$

Now substitute this expression for $y$ into the second equation:

$x^2 + y = 1$

$x^2 + (x + 1) = 1$

$x^2 + x + 1 = 1$

$x^2 + x = 0$

$x(x + 1) = 0$

This gives us two possible values for $x$:

$x = 0$ or $x + 1 = 0$ which means $x = -1$

If $x = 0$, then $y = x + 1 = 0 + 1 = 1$

If $x = -1$, then $y = x + 1 = -1 + 1 = 0$

Therefore, the solutions are $(0, 1)$ and $(-1, 0)$.

3. Final Answer

The solutions are $(0, 1)$ and $(-1, 0)$.